18.A. Discuss the existence of both the deleted and the non-deleted limit e following functions at the point x = 0. . (a) f(x) = |¤], (b) f(x) == 1/x, *# 0, (c) f(x) = x sin (1/x), x * 0, (x sin (1/7). * + 0.
18.A. Discuss the existence of both the deleted and the non-deleted limit e following functions at the point x = 0. . (a) f(x) = |¤], (b) f(x) == 1/x, *# 0, (c) f(x) = x sin (1/x), x * 0, (x sin (1/7). * + 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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18.A
Transcribed Image Text:18.A. Discuss the existence of both the deleted and the non-deleted limits of
the following functions at the point r = 0.
(a) f(x) = |c|,
* * 0,
I sin (1/x),
(x sin (1/x),
[1,
(b) f(x) = 1/x,
(c) f(x)
* + 0,
x* 0,
(d) f(x)
0,
(e) f(x)
sin (1/x),
x * 0,
'ol
x > 0.
I<0,
(f) f(x)
=
18.B. Prove Lemma 18.2.
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